MATH05L02: Rounding Off Numbers Up to Billions
OBJECTIVES
Round off numbers to the indicated place values
Solve problems involving rounding off numbers up to billions
LESSON PREREQUISITE
None.
LESSON PROPER
Rounding Off Numbers
Here are the steps in rounding off numbers: - Identify first the place value at which the number will be rounded off. - Mark the digit in this place value, then look to the next digit to the right. - If this digit is 0, 1, 2, 3, or 4, then we just retain the marked digit. This is rounding down. - If the digit to the right is 5, 6, 7, 8 or 9, - We increase the marked digit by one. This is rounding up.
Examples:
1. Round off 278 560 321 to the nearest million
Mark the digit at the place value of rounding off: 278 560 321
Look at the digit to its right: Next digit is 5.
Increase the marked digit by 1: The 8 changes to 9.
Then change all the succeeding digits to zero: 279 000 000
2. Round off 19 678 230 000 to the nearest billion.
Mark the digit at the place value of rounding off: 19 678 230 000
Look at the digit to its right: Next digit is 6.
Increase the marked digit by 1: The 9, increased by 1 is 10.
Therefore the “19” becomes “20”, and then change all the next
digits to the right to zeros: 20 000 000 000
Big numbers in billions and millions, when rounded off, sometimes
use decimal numbers to capture the portions of a billion or a million.
This same number, may be reported as 19.7 billion or 19.7 B. For example, in newspaper headlines: “Company ABC sold for 19.7 B”
In effect, this is rounding off to the nearest hundred million instead of
to the nearest billions.
Rounding Off in Problem Solving
In problem solving, you either round up first then solve, or solve first then
round off the result of the computation.
The place value to which the answer will be rounded off, are often indicated in the problem. Sometimes you’ll need to just decide on the most sensible rounding off for the answer.
Example:
The following is the global tally of COVID-19 cases, deaths and recoveries as of May 2021:
Cases: 163 726 962
Deaths: 3 393 551
Recovered: 142 198 031
About how many millions therefore were still active cases at that time?
To solve this, the first step will be to round off all these figures to the
nearest millions:
In nearest millions
Cases: 163 726 962 164 000 000
Deaths: 3 393 551 3 000 000
Recovered: 142 198 031 142 000 000
Add up the rounded off figures for deaths and recovered cases:
Deaths + Recovered: 3 M + 142 M = 145 M
Then subtract this from the rounded off figure for the total number of
cases:
164 M - 145 M = 19 M active cases. Rounding off the givens before they are used in computations make the computations simpler and faster.